Calculating Size of Star Image with Converging Lens

[Emilyjoint]

An image of a point source (star) at infinity produces an image using a converging lens of diameter 50mm and focal length 500mm. Calculate the diameter of the resulting image.(take wavelengthof light to be 4x10^-7m)
I ask this because it is to do with seeing stars through a telescope.
I think the diameter is caclulated using diffraction principles to be 8mm Can anyone check to see if you get the same answer.
I used Sinθ = λ/a

 

[Char. Limit]

A star is not a point source.

A star is a ball.

 

[davenn]

A star is not a point source.

A star is a ball.

That is essentially true, but because of the distances involved it can be regarded as a point source from an optical point of view

Dave

 

[Emilyjoint]

OK./...would a point source produce an image of this size?

 

[Drakkith]

How about this? http://www.calctool.org/CALC/phys/optics/f_NA

 

[Emilyjoint]

Looked at that but could not see how it relates to a point source.
S it OK to use Sin theta = λ/a to calculate th width

 

[Drakkith]

I don't have time to explain it at the moment, but take a look at the following article and it should help.

http://en.wikipedia.org/wiki/Airy_disk

 

[Emilyjoint]

Thanks for the help.Used the Calc site and got 9x10^-3mm...i had made a mistake with units.
got it now

 

[sophiecentaur]

OK./...would a point source produce an image of this size?

The size of image from a star is dependent on its relative magnitude (brightness) and the optics of your imaging system (diffraction and other aberrations). There is no clue about the angle subtended by it at the Earth.

(Most) planets in the Solar System subtend a big enough angle to distinguish the actual angular diameter of their disc (they look like little moons) but even the nearest star is a 'point' source to all intents and purposes.